Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, such procedures are only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.

翻译：对二元变量极值依赖关系的建模在环境规划、灾害建模和水文学等广泛的实际应用中具有重要意义。现有方法大多基于二元正则变化框架，已有大量文献研究该框架下依赖结构的估计问题。然而，此类方法仅适用于呈现渐近依赖性的变量，而实践中常观察到渐近独立性。本文研究所谓的“角依赖函数”——该量概括了渐近独立变量的极值依赖结构。直到最近，仅有角依赖函数的逐点估计方法可用。我们引入一系列全局估计方法，并通过系统仿真研究及英国英格兰北部河流流量数据的实例分析，将其与另一项最新提出的全局估计技术进行对比。